WDM telecommunication system, which is frequently used to transmit large bandwidth information, transmits the optical signal with ‘N’ number of wavelengths simultaneously through a single line of an optical fiber. Since the maximum bandwidth is carried out with a single optical fiber line in the long haul transmission, DWDM transmission is usually carried the many wavelengths which are separated by the certain spacing of 1.0 nm or less. The AWG (Arrayed Waveguide Grating) multiplexex/demultiplexer is frequently used at the end of receiver units to demultiplex the optical signal with multiplexed many wavelengths.
FIG. 1 represents the schematic illustration of the conventional Arrayed Waveguide Grating. The conventional AWG consists one (or more) stripe waveguide circuit (1) connected to the input slab waveguide from the input optical fiber, output waveguide circuits (2) to the output fibers from output slab waveguide, two of slab waveguides (3, 4) and arrayed waveguides (5) on a planar substrate (6). The multiplexed optical signal entered into the stripe waveguide circuit (1) connecting the input slab waveguide is spread out at the input slab waveguide (3) section by diffraction and the resultant signal is propagated into the arrayed waveguides (5) which have the different lengths of waveguides. Because of the propagation length differences among the adjacent waveguides, each light in each waveguide in the arrayed waveguides (5) section arrives at the output slab waveguide (4) with the different phase. The resultant light arriving at the output slab waveguide represent the linear line of the in-phase plane, and the optical signal of the different wavelengths makes the different slop of the linear line of the in-phase plane because of the wavelength-phase selectivity. Therefore, the optical signal of the different wavelength has the different position where the light condenses. Then the output waveguide circuits (2) from the output slab waveguide can be located at these light-condense positions to separate the multiplexed signal.
The operation theory can be simply illustrated by Formula (1):(ns*d*sin φ)+(nc*ΔL)=m*λ  (Formula 1)
wherein ns is the refractive index of the slap waveguide, d is the pitch of the waveguide in the arrayed waveguides section at the interface between arrayed waveguides and output slab waveguide, φ is the diffraction angle of propagation light from arrayed waveguides to the output slab waveguide, nc is the refractive index of the core of arrayed waveguides, ΔL is the difference of the length in the waveguides among the arrayed waveguides, m is the diffraction degree and λ is the wavelength of output light Therefore, the following Formula (2) can be derived from Formula (1) where center wavelength is defined to be the center of the light wavelength exiting out at the output waveguide circuit located at the 0 degree of diffraction angle, φ.λ0=nc*(Δλ/m)  (Formula 2)
The waveguide layer (14) of AWG mainly consists of silica glass material. Because the refractive index of the silica glass material can be changed with the temperature variation, the optical wavelength characteristics of AWG composed with such silica glass material waveguide can be changed upon the temperature variation. As well, the length of waveguides can be changed because the silicon substrate (6), which is the main substrate materials for AWG fabrication, experiences either thermal contraction or thermal expansion because of the temperature variation, and these thermal behaviors result the undesired center wavelength shift of the output demultiplexed light at the output waveguide circuits (2). To understand the temperature dependency of center wavelength, Formula 2 is differentiated by temperature term, T, and the result is shown as Formula 3.dλ/dT=(λ/nc)*(dnc/dT)+(λ/ΔL)*(dΔL/dT)=(λ/nc)*(dnc/dT)+(λ/as)  (Formula 3)
wherein as is the thermal expansion coefficient of the substrate.
The first term in Formula 3, (λ/nc)*(dnc/dT), expresses the temperature dependency of the refractive index of the waveguide. For example, the temperature dependency of the refractive index of the waveguide can be calculated as (λ/nc)*(dnc/dT)=0.0085 nm/K where the refractive index change of silica glass as a waveguide upon the temperature change, (dnc/dT), in general is 8×10−6/K, refractive index of waveguide is nc=1.45, and center wavelength is λ0=1550 nm. The second term, (λ/as), expresses the temperature dependency of wavelength upon the thermal expansion and contraction of the substrate (6). For example, the temperature dependency of the wavelength is λ/as=0.0036 nm/K where the CTE of silicon substrate is as=2.5×10−6/K. Therefore, the center wavelength shift upon the temperature variation is (dλ/dT)=0.012 nm/K. This calculated value is well matched with the measured value, 0.01 lnm/K, from the conventional AWG chip.